Predicting overstriding with wearable IMUs during treadmill and overground running

Running injuries are prevalent, but their exact mechanisms remain unknown largely due to limited real-world biomechanical analysis. Reducing overstriding, the horizontal distance that the foot lands ahead of the body, may be relevant to reducing injury risk. Here, we leverage the geometric relationship between overstriding and lower extremity sagittal segment angles to demonstrate that wearable inertial measurement units (IMUs) can predict overstriding during treadmill and overground running in the laboratory. Ten recreational runners matched their strides to a metronome to systematically vary overstriding during constant-speed treadmill running and showed similar overstriding variation during comfortable-speed overground running. Linear mixed models were used to analyze repeated measures of overstriding and sagittal segment angles measured with motion capture and IMUs. Sagittal segment angles measured with IMUs explained 95% and 98% of the variance in overstriding during treadmill and overground running, respectively. We also found that sagittal segment angles measured with IMUs correlated with peak braking force and explained 88% and 80% of the variance during treadmill and overground running, respectively. This study highlights the potential for IMUs to provide insights into landing and loading patterns over time in real-world running environments, and motivates future research on feedback to modify form and prevent injury.


Testing protocol
This protocol consisted of a treadmill (TM) running portion and an overground (OG) running portion (Fig. 1).Participants completed 30-s running trials on an instrumented TM set to 3.0 ms −1 , matching their strides to a metronome set to five different stride frequencies (SF): 75, 80, 85, 90 and 95 strides min −1 , in randomized order.The last 15 strides were used for analysis.Prior to data collection, participants completed 8 min of warm-up TM running at 3.0 ms −1 , which included 3 min at their self-selected SF followed by 1 min at each SF to become familiarized with the metronome.Following completion of the TM portion of the protocol, participants took a 5-min break and then completed three to four warm-up laps around a 36-m oval track with embedded force plates on one straightaway.Data was then recorded during a 5-min continuous OG running trial.During this trial, participants were instructed to run at a comfortable self-selected speed and SF.All strides on the force plates within 5% of the median speed over the 5-min OG trial were used for analysis (12.6 ± 1.4 strides).

Data collection
We collected data from optical motion capture, force plates, and IMUs for all 10 subjects during both TM and OG portions.Reflective markers were placed on anatomical landmarks on the pelvis (left and right iliac crests, left and right anterior superior iliac spines, left and right posterior iliac spines, and left and right greater trochanters), left leg (medial and lateral epicondyles of the femur, medial and lateral malleoli), and left foot (calcaneus, second and fifth metatarsal heads).Marker cluster plates were affixed to the lateral aspects of the left thigh, shank, and foot segments and used as tracking markers.An additional marker was placed on the suprasternal notch to measure running speed during the OG trial.A standing static trial was collected prior to running data collection.Marker data was recorded at 200 Hz using an infrared camera motion capture system (Oqus and Miqus, Qualysis Corp, Gothenburg, Sweden).Three-dimensional GRFs were simultaneously recorded at 2000 Hz using an instrumented treadmill and ground-embedded force plates (Bertec Corp, Columbus, OH).Foot contact times were identified when the vertical GRF exceeded 20 N and were used to determine gait cycle.
Participants wore three wireless IMUs (XSens Dot, Movella Inc, Henderson, NV, weight: 11.2 g, size: 36.3 mm × 30.4 mm × 10.8 mm) on the left thigh, shank, and foot, respectively, which were rigidly attached to the marker cluster plates on these segments.Motion data from the IMUs was recorded at 120 Hz, stored locally on each sensor, and downloaded after each session (accelerometer range: ± 16 g, gyroscope range: ± 2000 • /s, magnetometer range: ± 8 Gauss).A complementary phone app (XSens Dot, Movella Inc, Henderson, NV) was used to start and stop IMU data recording.

Data processing
Kinematic and kinetic data from optical motion capture and force plates were analyzed using Visual 3D (C-Motion, Germantown, MD).Motion capture marker data were low-pass filtered using a bidirectional, fourth-order Butterworth filter with a cutoff frequency of 10 Hz.Force data were filtered with a 50 Hz low-pass filter.Besides the manufacturer's proprietary onboard filtering algorithms, no additional filters were applied to the IMU data.
The 3D orientation data provided by the IMUs was calibrated to a standing pose at the start of the TM trials to better compare to the motion capture data.Since IMU orientation outputs are known to be susceptible to drift, as error is accumulated around the IMU global gravity axis over time, we implemented a different calibration procedure for the OG trial.To manage drift over the 5-min trial, the IMU data was calibrated according to several assumptions 22 .We first assumed that the hip, knee, and ankle were perfect hinge joints, such that all relevant motion of the thigh, shank, and foot occurred in the sagittal plane during running.Based on IMU sensor placement on the lateral aspect of each segment, we assumed that one of the IMU local coordinate axes was aligned with the joint axis and that all relevant segmental rotations were about this axis.At each time frame, we redefined the IMU global reference frame with one axis aligned with the joint axis and another pointed against gravity.We estimated the rotation between the local and the updated global IMU frames, and defined each segment's sagittal angle as the Euler angle corresponding to rotation about the joint axis.
Across participants, the IMUs started recording after the motion capture data, with a range of delays from 90 to 180 ms.IMU data was synchronized to motion capture data by maximizing the cross-correlation between the segment angles during a calibration maneuver performed before each trial (hard step with the left foot followed by a forward and backward swing of the left leg).Time-aligned IMU and motion capture data were used for all analyses.

Metric definitions
Several metrics were analyzed in this study (Fig. 2).Overstriding refers to the horizontal distance between the greater trochanter marker and the lateral malleolus marker.To compare across participants, this distance was normalized by leg length.θ Thigh,FC , θ Shank,FC , and θ Foot,FC refer to the sagittal thigh, shank, and foot angles at foot contact (FC) derived from Visual 3D with respect to the laboratory global frame.Sagittal thigh and shank angles from motion capture are referenced to vertical, with a positive θ Thigh,FC or θ Shank,FC indicating that the segment is in front of its proximal endpoint.Sagittal foot angle from motion capture is referenced to horizontal (e.g. the floor), with positive θ Foot,FC indicating a rear-foot strike and negative θ Foot,FC indicating a fore-foot strike.θ Thigh IMU,FC , θ Shank IMU,FC , and θ Foot IMU,FC refer to the sagittal thigh, shank, and foot angles at FC derived from IMUs.θ Thigh IMU,FC and θ Shank IMU,FC are measured with respect to vertical, and θ Foot IMU,FC is measured with respect to horizontal.Peak braking force (PBF) refers to the peak of the posterior GRF.

Statistical analysis
We compared sagittal segment angles computed with IMU orientations to sagittal segment angles from motion capture at foot contact using root mean square error (RMSE).Linear mixed model (LMM) regressions were performed to quantify the relationship between sagittal segment angles at foot contact and overstriding as well as sagittal segment angles at foot contact and PBF during TM and OG running (Table 1).
As overstriding is a global distance measurement, the sum of segment lengths multiplied by the sine of sagittal segment angles would be required to measure overstriding directly.While segment lengths are easily measured using motion capture markers placed at proximal and distal endpoints, this study sought to use IMUs alone to predict overstriding.Therefore we included only sagittal segment angles as predictors in the LMMs.
LMM regressions were chosen to account for repeated measures on the same individuals 13 .These models are known as "mixed" models because they contain both fixed effects and random effects, with the latter accounting for individual differences in response.LMM regressions follow the form: where Y i is the dependent or response variable, X i is the independent or predictor variable, β is the fixed effect coefficient, Z i is Figure 2. Illustration of data processing and metric definitions from exemplary time-aligned data for a single participant during a treadmill running trial.θ Thigh,FC (green) and θ Shank,FC (blue) represent the sagittal thigh and shank angles relative to vertical at foot contact (FC), where a positive value indicates that the segment is in front of its proximal endpoint.θ Foot IMU,FC (orange) represents the sagittal foot angle relative to the floor at FC, where a positive value indicates a rear-foot strike and a negative value indicates a fore-foot strike.Overstriding (OS) is the horizontal distance between the greater trochanter and the lateral malleolus marker at FC and is geometrically related to θ Thigh,FC and θ Shank,FC .Peak braking force (PBF) is computed from the anterior- posterior ground reaction force (GRF AP ) measured by force plates, shown in red.In the time series plots, shaded gray vertical lines represent FC events.Solid lines represent sagittal segment angles measured from motion capture marker data (Mocap), and black dashed lines represent sagittal segment angles measured from inertial measurement units (IMU).We observed high alignment between the synced Mocap and IMU data.www.nature.com/scientificreports/ the grouping variable, α i is the random effect coefficient, ǫ i is an error term, and i = 1, ..., N .Participant identifier was the grouping variable in all models, and N was the total number of strides used in the analysis.All model inputs were standardized as Z scores and fit using the restricted maximum likelihood (REML) estimator in R's lme4 package.Each LMM was fit as a random-intercept model, so participant-specific intercepts were identified.For the fixed effects, we reported coefficients, 95% confidence intervals (CI), and p values.Significance was set at p < 0.05.For the random effect, we reported the intraclass correlation coefficient (ICC), which quantifies the proportion of variance explained by the participant identifier.Marginal R 2 and conditional R 2 values were calculated to assess model fit.Marginal R 2 accounts for only the variance of the fixed effects, while conditional R 2 incorporates variance of both fixed and random effects 23 .

Participants varied overstriding during TM and OG running
During the TM portion of the protocol, participants ran at a constant speed of 3.0 ms −1 and were able to match their strides to the prescribed stride frequencies (SF) (Supplementary Table 1).As SF increased, both overstriding and PBF decreased (Fig. 3).The mean range of overstriding for each participant throughout all TM trials was 5.9 ± 1.3 cm (mean ± standard deviation).The mean range of PBF was 0.18 ± 0.05 BW.While the TM trials enabled us to systematically modulate overstriding using a previously published methodology 13 , this work observed stride-to-stride variability in overstriding during OG running at a self-selected comfortable speed (2.9 ± 0.27 ms −1 ) and SF (81 ± 3.5 strides min −1 ).The mean range of overstriding throughout the OG trial for each participant was 3.8 ± 1.3 cm, and 0.09 ± 0.02 BW for PBF.Overstriding varied less during OG running, which was expected as neither stride frequency, stride length, nor speed was modulated during this portion of the protocol.
We also inspected the ranges of sagittal segment angles at foot contact during TM and OG running.Participants modulated thigh angle by 6.0 ± 1.7 • , shank angle by 7.2 ± 1.4 • , and foot angle by 8.9 ± 2.1 • during TM running.In general as SF increased, sagittal segment angles at foot contact decreased (Supplementary Table 1).During OG running, participants modulated thigh angle by 3.6 ± 1.6 • , shank angle by 4.2 ± 1.4 • , and foot angle by 4.7 ± 2.1 • .The range of sagittal segment angles during the OG trial was lower than that of the TM trials.Given the geometric relationship between sagittal segment angles and overstriding, it aligns that the range of both overstriding and sagittal segment angles were lower in OG running than in TM running.

Sagittal segment angles from motion capture correlated with overstriding during TM and OG running
Thigh and shank angle at foot contact significantly contributed to a model of overstriding during TM running (p: <0.001 for both) but not foot angle (p: 0.054) (Table 2, LMM 1A).Marginal and conditional R 2 were 83.0% and 98.8%, respectively (Table 2, LMM 1A).During OG running, thigh and shank angle at foot contact significantly contributed to a model of overstriding (p: <0.001 for both) but not foot angle (p: 0.202) (Table 2, LMM 2A).Marginal and conditional R 2 were 86.4% and 99.4%, respectively (Table 2, LMM 2A).

Discussion
The purpose of this study was to demonstrate that wearable IMUs can predict overstriding during running and then to investigate if such IMU-derived overstriding metrics correlate with braking force metrics.Before using IMU data, we first confirmed that overstriding can be represented by lower extremity sagittal segment angles measured from motion capture, as geometrically expected, during both TM and OG running.Comparing the marginal and conditional R 2 values of the TM and OG models enables us to understand the predictive performance of the sagittal segment angles for overstriding measurement.We found that θ Thigh,FC and θ Shank,FC correlated with overstriding during TM running, explaining 83% and 99% of the marginal and conditional variance, respectively, and during OG running, explaining 86% and 99% of the marginal and conditional variance, respectively.θ Foot,FC did not significantly contribute to these models (Supplementary Fig. 1).From the marginal variance explained in this dataset, we expect that thigh and shank angles measured from additional participants would show good predictive performance for overstriding.
After demonstrating that sagittal segment angles measured from motion capture are correlated with overstriding, we showed that IMUs can be used to measure these angles.The error between motion capture and IMU measurement for sagittal segment angles at foot contact was less than 5 • for all segments for both TM and OG running, which is similar in magnitude to what has previously been reported 24 .We therefore considered the IMU sagittal segment angles to be reasonable.To demonstrate the potential for assessing overstriding outside of a laboratory environment, we showed that IMUs worn on the thigh and shank can predict overstriding during TM running, explaining 56% and 95% of the marginal and conditional variance, respectively, and during OG running, explaining 62% and 98% of the marginal and conditional variance, respectively.These results are www.nature.com/scientificreports/lower than the marginal variance explained by motion capture angles (83% TM and 86% OG).Based on the magnitude of the measurement errors between motion capture and IMU sagittal segment angles during TM and OG running, we expect that the models using IMU angles would have similar but worse performance to those using motion capture.
To further highlight the potential utility of wearable sensors that measure sagittal segment angles, we evaluated the relationship between these angles and braking force, a commonly reported metric in running injury literature.We leveraged the established relationship between overstriding and braking during TM running 13 to understand how sagittal segment angles first contribute to overstriding and then subsequently to PBF.We found that sagittal segment angles measured from IMUs correlated with PBF during both TM and OG running.θ Thigh IMU,FC , θ Shank IMU,FC , and θ Foot IMU,FC significantly contributed to a model of PBF, explaining 43% and 88% of the marginal and conditional variance, respectively during TM running and 36% and 80% of the marginal and conditional variance, respectively during OG running.These results are similar to the marginal variance explained by motion capture sagittal segment angles (46% TM and 40% OG).These results are also comparable to recent studies which explained 52% of the variance in cumulative braking impulse during TM running using commercial wearable sensors on the wrist and chest 25 .
While neither θ Foot,FC nor θ Foot IMU,FC significantly contributed to overstriding during OG running, this seg- ment angle did significantly contribute to PBF.The landing angle of the foot may therefore provide additional information to explain braking force, after accounting for overstriding measured by thigh and shank sagittal angles.This finding is similar to a previous study that showed both distance from COM to heel (overstriding) and foot strike angle are kinematic predictors of PBF, explaining 57% of the variance during TM running along with self-selected speed and stride length as predictors 21 .A sub-analysis of our OG data showed that a model with only θ Thigh IMU,FC and θ Shank IMU,FC as predictors explained 43% of the marginal variance of PBF (compared to 36% with the addition of θ Foot IMU,FC ), while a model with θ Shank IMU,FC as the only predictor still explained 26% of the marginal variance.
Understanding the relative contribution of each segment to overstriding per individual across multiple speeds and slopes would be useful to determine the minimal sensor set required to achieve biomechanically-relevant, robust information on running form.When considering a minimal sensor set, it is helpful to target sensor placement based on which metrics are most desired.For example, using thigh and shank IMUs have been used to predict knee stiffness 26 , a metric found to be related to injury in a prospective study 27 , while also providing information about overstriding and braking force.Runners with tibial stress fractures were found to have higher peak tibial acceleration values compared to uninjured runners 28 , which can be measured with an IMU on the shank 29 , and an additional IMU on the thigh could help elucidate the role of the knee in shock attenuation and injury, especially over a prolonged run 30 .
While this study focused on measuring overstriding with IMUs, recent prospective studies have identified other spatiotemporal and kinematic metrics related to bone stress injuries, namely step rate 31 , vertical excursion 31 , and duty cycle 32,33 (contact time divided by stride time).Duty cycle has previously been demonstrated to predict PBF, explaining 43% of the variance in a cohort of recreational runners 34 .A sub-analysis of our data showed that duty cycle, θ Thigh IMU,FC , and θ Shank IMU,FC significantly contribute to a model of PBF and can explain 59% of the marginal variance during OG running (compared to 43% with only θ Thigh IMU,FC and θ Shank IMU,FC as predictors and 26% with only duty cycle as a predictor).This study ultimately evaluated the relationship between landing position and braking during running, with the assumption that braking is relevant to injury 35 and therefore landing position (and degree of overstriding) is also relevant to injury.Recent systematic reviews show a lack of consensus on the relationship between braking force and injury [36][37][38] , but given that bone is susceptible to failure under shear stress 39 , monitoring braking force is likely still relevant to injury 40 .In this study, we measured peak braking force, but other metrics exist, i.e. impulse, time to peak, rate, etc. Developing models to estimate shear loading on the tibia and foot, similarly to previous models for compressive loading 41 , could provide more insight into cumulative loading and bone or tissue damage occurring during running.
In addition to monitoring running form for injury prevention, measuring overstriding and braking using wearable sensors may have applications in running economy 42 and performance 19 .Deceleration of the COM at impact may influence metabolic cost 42 , indicating that the length of the braking phase may be important to overall running efficiency.However, a study analyzing video-based kinematics and race performance during an elite marathon did not find any differences in overstriding between the final laps 19 .Only two strides per participant could be compared due to limitations in video capture volume of the race course, so using wearable sensors in similar future studies of fatigue and performance could enable a more continuous measurement of overstriding.
Interestingly this same study analyzing race-based kinematics did find differences between genders, with women having greater relative "foot ahead" distance.Although our dataset is not large enough to compare gender groups, we saw that shorter leg lengths resulted in greater overstriding and greater braking, and women tend to have shorter legs compared to the men in this study (0.86 m vs. 0.92 m).This relationship is expected at constant speed TM running but interestingly during OG comfortable speed running, those with shorter legs still exhibited greater PBF.This finding is in agreement with a previous study that found leg length to be a significant contributor to a model of PBF during OG running 43 .More participants would be needed to study gender differences in overstriding and loading patterns.
There were several limitations in this study.This study was conducted in a controlled laboratory environment on level ground to validate IMU-based measurements against an accepted ground truth; however, further study is needed to demonstrate similar results in less controlled spaces, including variable speeds, slopes, and terrains.We found that the IMU errors are not consistent across segments or stride frequencies (Supplementary Table 1), suggesting sensor noise may be influenced by running parameters.Moreover, the sensitivity of these results to IMU placement across longer durations or across days warrants additional study to provide repeatable, reliable measurements of overstriding.Participants were instructed to wear their typical running shoes to eliminate confounding factors from comfort.However, differences in shoe stiffness may introduce errors or inconsistencies in the braking force measurements 44 .In this laboratory evaluation, we used force plates to segment the gait cycle.Detecting foot contact with IMUs has been demonstrated during running 45 and implementing this gait segmentation would be necessary for outdoor investigations of overstriding.
This study measured only 10 recreational runners, and given that overstriding can occur in both fore-foot and rear-foot strikers, we did not restrict our inclusion to participants with a specific foot strike pattern.During TM and OG running, we found that those who landed with "extreme" angles, i.e. greater than 10° of plantarflexion or greater than 10° of dorsiflexion, exhibited greater overstriding distances than those who landed with a more neutral foot-to-floor angle.A recent study using an unsupervised learning approach to cluster biomechanical data found that collegiate runners with more than 10° of plantarflexion at landing had a higher incidence of bone stress injuries compared to other less-plantarflexed groups 33 .While overstriding was not explicitly reported, we could posit from our results that the excessively plantarflexed group was overstriding more than the groups who landed closer to neutral.More participants representing the continuum of angles would be needed before we can draw conclusions about the impact of foot strike pattern on overstriding and on injury risk 3 .Further, there is currently no consensus on what qualifies as excessive overstriding, so more real-world tracking with wearable sensors and longitudinal studies are needed.
A next step is to use IMUs to predict overstriding in natural running environments.Managing noise and drift in IMU measurements will be necessary for long term use, and practices to improve accuracy have begun to be established 46,47 .Some considerations for measurement accuracy include developing calibration routines to minimize effects of IMU placement or movement due to soft tissue artifacts.In addition to focusing on sensor signal robustness, minimizing the number of sensors needed to provide informative data is important to enable larger scale implementation and data collection, for example within a collegiate cross-country team or community run club.Future work could consider using biofeedback to reduce overstriding and subsequently braking force.Previous work has demonstrated the potential for biofeedback in reducing tibial shock during TM running using visual feedback 48 and during OG running using music 49 .
While overstriding is correlated with PBF, developing estimates of anterior-posterior GRF for ground-truth comparison in environments outside of the laboratory is important to better understand loading during long distance running.Likely sensor fusion with pressure insoles and individualized machine learning approaches will be needed, in addition to kinematic measures from IMUs 50 .This multi-modal approach has shown promise in estimating vertical 51 and 3D 52 GRF metrics and cumulative tibial loading 53 .By establishing which metrics are currently most relevant to injury and which wearable sensors can be used to yield these data, we can begin to conduct more sensorized prospective injury studies and gain more insights into the mechanisms behind running injury development.

Figure 1 .
Figure 1.Schematic showing placement of motion capture markers and inertial measurement units (IMUs) worn during running on (a) an instrumented treadmill (TM) and (b) an overground (OG) laboratory track with ground-embedded force plates.Sagittal segment angles were measured from motion capture and IMUs, and ground reaction forces were collected from force plates.Participants completed TM running at 3 ms −1 and matched their strides to a prescribed stride frequency (SF) using a metronome.Participants ran at a self-selected comfortable speed and SF during the OG portion of the protocol.(c) Timeline of experimental protocol.Data was recorded during the five 30-s SF-randomized TM trials and one 5-min OG trial.

Figure 3 .
Figure 3. Box and whisker plots showing the distribution of overstriding and peak braking force (PBF) measured at each prescribed stride frequency (SF) during treadmill running.Each box extends from the first to third quartile of the data, with a horizontal line at the median.The whiskers extend from the box to 1.5 times the interquartile range.

Table 2 .
Linear mixed model (LMM) results.In each LMM, sagittal segment angles at foot contact (FC) are the fixed effects, participant identifier is the random effect, and either overstriding (OS) or peak braking force (PBF) is the dependent variable.Results are shown for data collected during treadmill (TM) and overground (OG) running.The top row (A) reports sagittal segment angles measured from motion capture, denoted as θ Thigh,FC , θ Shank,FC , and θ Foot,FC .. The bottom row (B) reports sagittal segment angles measured by IMUs, denoted as θ Thigh IMU,FC , θ Shank IMU,FC , and θ Foot IMU,FC .P values < 0.05 are in bold.